Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
int main(void)
{
	priority_queue<int> que;
	int n,a[1000];
	int i,j,k;
	int M[4],sum,cnt;
	double Max;
	cin>>n;
	for(i=0;i<n;i++){
		cin>>a[i];
		que.push(a[i]);
	}
	for(i=0;i<4;i++){
		M[i]=que.top();
		que.pop();
	}
	Max=-1;
	for(i=0;i<n;i++){
		for(j=0;j<n;j++){
			if(i==j||a[i]<a[j]) continue;
			cnt=0; sum=0;
			for(k=0;k<4;k++){
				if(M[k]!=a[i]&&M[k]!=a[j]){
					cnt++;
					sum+=M[k];
				}
				if(cnt==2) break;
			}
			if(Max<(double)sum/(a[i]-a[j])) Max=(double)sum/(a[i]-a[j]);
		}
	}
	printf("%lf\n",Max);
	return 0;
}